The Conditional Location of a Median Path
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Finding r-Dominating Sets and p-Centers of Trees in Parallel
IEEE Transactions on Parallel and Distributed Systems
Conditional location of path and tree shaped facilities on trees
Journal of Algorithms
Efficient algorithms for a constrained k-tree core problem in a tree network
Journal of Algorithms
Finding the conditional location of a median path on a tree
Information and Computation
Conditional location of path and tree shaped facilities on trees
Journal of Algorithms
Efficient algorithms for a constrained k-tree core problem in a tree network
Journal of Algorithms
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Let T be an edge-weighted tree. A p-core of T is a set of p mutually disjoint paths in T that minimizes the sum of the distances of all vertices in T from any of the p paths, where $p \geq 1$ is an integer. In this paper, an O(n) time algorithm is proposed for the case p = 2, where n is the number of vertices in T. Our algorithm improves the two O(n2) time algorithms previously proposed by Becker and Perl [Discrete Appl. Math., 11 (1985), pp. 103--113]. With some modifications, the proposed algorithm can be implemented on the EREW PRAM in O(log2 n) time using O(n log n) work.